1. Field of the Invention
The present invention relates to an induction motor drive without a speed sensor and/or a rotational position sensor, and more particularly, to an observer for vector-controlling an induction motor drive.
2. Description of the Related Art
A typical vector control system for a direct field-oriented induction motor drive without a speed sensor and/or rotational position sensor is shown in FIG. 1.
In the system without a speed sensor, only a stator voltage 206 and a stator current 207 are detected by sensors 108 and 109.
Vector control for an induction motor 100 in this figure is performed based on the torque of the induction motor 100, which is independently applied, and the magnetic flux fed by an inverter 101.
With the vector control in the system shown in this figure, a speed regulator 107 generates a torque current reference 202 under PI control (proportional action and integral action control) from a an estimated speed reference 200 being an instruction of the speed of the motor, and an estimated speed 211 from a flux and speed observer 110 as a feedback, and outputs the generated torque current reference 202 to a current regulator 106. The current regulator 106 outputs a current that is regulated under the PI control from the torque current reference 202 being an instruction to the torque and a flux current reference 201 being an instruction to the magnetic flux. Then, a vector rotator 104 transforms this current value into a relative value in a coordinate system (d-q coordinate system) that rotates in synchronization with a synthesized current vector, and applies the transformed value to the inverter 101 as a primary voltage command 205. The flux current reference 201 applied to the current regulator 106 can be set to a constant value over a wide operation range while the torque current reference 202 is generated by a PI loop according to the estimated speed 211.
The voltage and the current values applied from the inverter 101 to the induction motor 100 are detected as the detected voltage 206 and the detected current 207 by the sensors 108 and 109. After the detected voltage 206 and the detected current 207 are transformed into values represented by a two-phase coordinate system by 3-2 phase transformers 102 and 103, they are input to the flux and speed observer 110 as space vector values vs 208 and is 209.
The flux and speed observer 110 obtains an observed rotor flux 210 from the stator voltage vs 208 and the stator current is 209, outputs the obtained flux 210 to vector rotators 104 and 105, estimates a rotor speed, and outputs the estimated speed 211 to the speed regulator 107.
The vector rotator 104 vector-rotates a flux command 203 and a torque command 204 in the orientation of the rotor flux based on the observed rotor flux 210, and outputs the vector-rotated commands to the inverter 101 as the primary voltage instruction 205.
Additionally, the vector is 209 is vector-rotated by the vector rotator 105 in the orientation of the rotor flux based on the observed flux 210 from the flux and speed observer 110 in order to obtain a flux current 212 and a torque current 213, which are used as feedback signals by the current regulator 106.
An MRAS (Model Reference Adaptive System) based on a flux and speed observer was initially proposed by Ref. 1.
Ref. 1: H. Kubota et al. xe2x80x9cDSP-based speed adaptive flux observer of induction motorxe2x80x9d, IEEE Trans. Industry Applicat., vol. 2, no. 2 pp. 343-348, 1993.
According to Ref. 1, a stator current and a rotor flux are used as an independent set of variables in order to explain an induction motor. Accordingly, an equation for an induction motor, which is demonstrated by Ref. 1, can be rewritten to an equation using a stator flux and a rotor flux as state variables. Since the process of this rewrite is a standard linear transformation, it is omitted here.
A classical representation of an induction machine in a stator oriented reference coordinate system (xcex1-xcex2) using a state space notation is as follows.                     {                                                                                                  ⅆ                                          ⅆ                      t                                                        ⁢                                      (                                                                  φ                        s                                                                    φ                        r                                                              )                                                  =                                                                                                    (                                                                                                                                                                              -                                                                      R                                    s                                                                                                  ⁢                                                                  L                                  sg                                                                ⁢                                I                                                                                                                                                                                      R                                  s                                                                ⁢                                                                  L                                                                      m                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                    g                                                                                                  ⁢                                I                                                                                                                                                                                                                                          R                                  r                                                                ⁢                                                                  L                                                                      m                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                    g                                                                                                  ⁢                                I                                                                                                                                                                                                                          -                                                                          R                                      r                                                                                                        ⁢                                                                      L                                    rg                                                                    ⁢                                  I                                                                +                                                                                                      ω                                    r                                                                    ⁢                                  J                                                                                                                                                                    )                                            ·                                              (                                                                                                                                            φ                                s                                                                                                                                                                                                        φ                                r                                                                                                                                    )                                                              +                                                                  (                                                                                                            I                                                                                                                                          0                                                                                                      )                                            ·                                              v                        s                                                                              =                                      Ax                    +                    Bu                                                                                                                                            i                  s                                =                                                                            (                                                                                                    L                            sg                                                    ⁢                          I                                                -                                                                              L                                                          m                              ⁢                                                              xe2x80x83                                                            ⁢                              g                                                                                ⁢                          I                                                                    )                                        ·                                          (                                                                                                                                  φ                              s                                                                                                                                                                                          φ                              r                                                                                                                          )                                                        =                  Cx                                                                                        (        1        )            
where:
xcfx86s=[xcfx86sxcex1 xcfx86sxcex2]T, xcfx86r=[xcfx86rxcex1 xcfx86rxcex2]T, is=[isxcex1 isxcex2]T, vs=[vsxcex1 vsxcex2]T
are space vectors associated with a stator flux, a rotor flux, a stator current, and a stator voltage respectively.
Other symbols are as follows.             L      sg        =                  1                  σ          ·                      L            s                              =                        L          r                                                    L              s                        ·                          L              r                                -                      L            m            2                                          L      rg        =                  1                  σ          ·                      L            r                              =                        L          s                                                    L              s                        ·                          L              r                                -                      L            m            2                                          L              m        ⁢                  xe2x80x83                ⁢        g              =                            1          -          σ                          σ          ·                      L            m                              =                        L          m                                                    L              s                        ·                          L              r                                -                      L            m            2                                          I      =              [                                            1                                      0                                                          0                                      1                                      ]              ;          xe2x80x83        ⁢          J      =              [                                            0                                                      -                1                                                                        1                                      0                                      ]              ;          xe2x80x83        ⁢          0      =              [                                            0                                      0                                                          0                                      0                                      ]              ;  
Rs, Rr: Stator and rotor resistance;
Ls, Lr, Lm: Stator, rotor, and mutual inductance;
"sgr"=1xe2x88x92Lm2/(Lsxc2x7Lr): Total leakage coefficient;
xcfx89r: Angular rotor speed.
Furthermore, according to Ref. 1, observed flux values are represented as follows. Note that observation and an observed value referred to in this specification represent observation and an observed value in modern control theory, and indicate the estimation of a state variable value from an output and its estimated value. In the following equation, observed values are marked with xe2x80x9c{circumflex over ( )}xe2x80x9d.                     {                                                                                                  ⅆ                                          ⅆ                      t                                                        ⁢                                      (                                                                                                                                                      φ                              ^                                                        s                                                                                                                                                                                                          φ                              ^                                                        r                                                                                                                )                                                  =                                                                            (                                                                                                                                                                  -                                                                  R                                  s                                                                                            ⁢                                                              L                                sg                                                            ⁢                              I                                                                                                                                                                          R                                s                                                            ⁢                                                              L                                                                  m                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                  g                                                                                            ⁢                              I                                                                                                                                                                                                                          R                                r                                                            ⁢                                                              L                                                                  m                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                  g                                                                                            ⁢                              I                                                                                                                                                                                                            -                                                                      R                                    r                                                                                                  ⁢                                                                  L                                  rg                                                                ⁢                                I                                                            +                                                                                                                                    ω                                    ^                                                                    r                                                                ⁢                                J                                                                                                                                                        )                                        ·                                          (                                                                                                                                                                  φ                                ^                                                            s                                                                                                                                                                                                                          φ                                ^                                                            r                                                                                                                          )                                                        +                                                            (                                                                                                    I                                                                                                                                0                                                                                              )                                        ·                                          v                      s                                                        +                                                                                                                                              (                                                                                                                                                                                      k                                1                                                            ⁢                              I                                                        +                                                                                          k                                2                                                            ⁢                              J                                                                                                                                                                                                                                                                      k                                3                                                            ⁢                              I                                                        +                                                                                          k                                4                                                            ⁢                              J                                                                                                                                            )                                    ·                                      (                                                                                            i                          ^                                                s                                            -                                              i                        s                                                              )                                                  =                                                                            A                      ^                                        ⁢                                          xe2x80x83                                        ⁢                                          x                      ^                                                        +                                      B                    ⁢                                          xe2x80x83                                        ⁢                    u                                    +                                      K                    ⁢                                          xe2x80x83                                        ⁢                                          e                      i                                                                                                                                                                                    i                    ^                                    s                                =                                                                            (                                                                                                    L                            sg                                                    ⁢                          I                                                -                                                                              L                                                          m                              ⁢                                                              xe2x80x83                                                            ⁢                              g                                                                                ⁢                          I                                                                    )                                        ·                                          (                                                                                                                                                                  φ                                ^                                                            s                                                                                                                                                                                                                          φ                                ^                                                            r                                                                                                                          )                                                        =                                      C                    ⁢                                          x                      ^                                                                                                                              (        2        )            
An output feedback gain K in the equation (2) is used to modify the dynamic characteristics of an estimation error and its determination.
The speed is evaluated with the following equation.                                           ⅆ                          ⅆ              t                                ⁢                                    ω              ^                        r                          =                                                            k                ω                            ·                              (                                                                            i                      ^                                        s                                    -                                      i                    s                                                  )                                      xc3x97                                          φ                ^                            r                                =                                    k              ω                        ·                                          φ                ^                            r              T                        ·            J            ·                          e              i                                                          (        3        )            
where kxcfx89 is an arbitrary gain.
According to Ref. 1, the feedback gain K in the observer equation (2) is used along with a constant of proportionality k in order to obtain four eigenvalues xcexobs of the flux observer represented by the equation (2), which are proportional to an eigenvalue xcexmot of the corresponding motor represented by the equation (1).
xcexobs=kxc2x7xcexmotxe2x80x83xe2x80x83(4)
The equation (4) is proved in the following document.
Ref. 2: Y. Kinpara and M. Koyama, xe2x80x9cSpeed Sensorless Vector Control Method of Induction Motor Including A Low Speed Region,xe2x80x9d The Journal xe2x80x9cDxe2x80x9d of the Institute of Electrical Engineers of Japan, vol. 120-D, no. 2, pp. 223-229, 2000.
With a selection method for a feedback gain K, which is proposed by Ref. 2, several unstable operation conditions are imposed on the induction motor. Especially, when a stator frequency approaches xe2x80x9c0xe2x80x9d, an observer does not converge, leading to inability of the operations of the motor drive.
An unstable region on a torque-speed plane of the induction motor drive depends on the value of the constant of proportionality k in the equation (4). This unstable area converges to a single line corresponding to the primary frequency that is exactly xe2x80x9c0xe2x80x9d when the constant k converges to xe2x80x9c0xe2x80x9d. Accordingly, the dynamic characteristics resultant from the flux observer become unacceptably slow for a very small value of k. Therefore, this selection method for the feedback gain K is not a good solution.
Ref. 2 proposes a method based on a Riccati equation as a selection method for the output feedback gain K in the equation (2), which stabilizes the drive.
With this method, if G, Q, and R are defined as follows       G    =          [                                    0                                0                                                0                                J                              ]        ;      xe2x80x83    ⁢      Q    =          [                                    I                                0                                                0                                I                              ]        ;
the output feedback gain K is obtained with the following equation.
K=PCTRxe2x88x921
where P is a sole positive definite solution that satisfies the following equation.
PAT+APxe2x88x92PCTRxe2x88x921CP+GQGT=0
With the method using the Riccati equation, the stability of the flux and speed observer is improved, but one arbitrary parameter (xcex51) that is not directly related to the stability of a global operation must be selected to obtain the output feedback gain. If this parameter is unsuitably selected, the observer can possibly be made unstable or an unacceptably large delay can possibly be caused. In either case, a resultant operation cannot run at a very low primary frequency.
The present invention was developed to overcome the above described problems, and aims at providing a control system, an observer, and a control method for an induction motor drive without a speed sensor or a position sensor, the operations of which are stable for global operation frequencies.
The present invention assumes a device or a method performing vector control for an induction motor that does not comprise at least either a speed sensor or a position sensor.
The control system according to the present invention comprises an observer unit and a control unit.
The observer unit determines a feedback gain K by using an estimation error of a stator current, and obtains and outputs at least either of an observed magnetic flux and an estimated speed based on the feedback gain K.
The control unit controls the induction motor based on the output of the observer unit.
With this system, only the restriction on the determination of the feedback gain K is, for example, an equation             lim              ω        →        0              ⁢          ∠      ⁢              xe2x80x83            ⁢                        G          l                ⁡                  (          jω          )                      =  ∞
That is, the feedback gain K which satisfies a condition based on a different factor can be determined with almost no restrictions.
Furthermore, the observer unit can be configured to determine the feedback gain K the magnitude of which is within a predetermined range, if the rotation speed of the induction motor is equal to or higher than a preset speed.
With this configuration, a stable operation can be realized even at an operating frequency in the vicinity of xe2x80x9c0xe2x80x9d.